Use the derivative of the function shown below to determine the open intervals in which the function is increasing or decreasing and any relative extrema, and the x-values at which the extrema occur. f(x) = ,x + 25x + 10

Q: Use the first derivative test and the second derivative test to determine where each function is…

A:

Q: Find the derivative of the function and evaluate  f '( x) at the given value of x.…

A:

Q: Q3\ Find the derivative of the following function by using the definition f(x) = x-1

A: Given function is fx=xx-1

Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

A: Here's the solution, please have a look at it...

Q: 16. Use the definition of the derivative to find the derivative of the function f(x) = 3/x and g(x)…

A: Given,

Q: Use limits to find the derivative function ƒ′ for the followingfunctions f.b. Evaluate ƒ(a)for the…

A: The derivative is,

Q: Find the derivative of the function using the power rule. (a) f(x) = 3/5x5 − 4x −4/3x-3 (b) f(x) =…

A: a) f(x)=35x5-4x-43x-3 f'(x)=ddx35x5-4x-43x-3       =35ddx1x5-4ddxx-43ddx1x-3…

Q: Let f(x) = x6, x ≤ 1 √√x, x > 1 Determine whether f is differentiable at x = 1. If so, find the…

A: Given :fx=x6,x≤1x6,x>1to check differentiable at x=1

Q: 1. f(x) = x² at x = 3

A: Given: f(x)=x2 at x=3

Q: Use the first derivative test to determine the local extrema, if any, for the function f(x) = 3(x -…

A: Given that a function f(x) and we find local extrema. For local extrema we do first derivative of…

Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

A: We have to determine the relative extreme values of the function using the first derivative test.

Q: Use the first derivative test and the second derivative test to determine where each function is…

A: The given function y=3x+4 Differentiate with respect to x f'(x)=323x+4 f'(x) is not defined at…

Q: Let f(x)= 3x^2+x-5. Using the definition of the derivative, find f’(x).

A:

Q: Use limits to find the derivative function ƒ′ for the followingfunctions f.b. Evaluate ƒ(a)for the…

A: fx=5x+2

Q: Find the derivative of the function and evaluate f(x) at the given value of x  f(x)=(3x-2)(x^2+3);…

A: Use the derivative of the form f = uv.

Q: Use the definition of the derivative to determine the derivatives of the following functions.   a.…

A: Part a,Given,         fx=1x3

Q: If f is a differentiable function, find an expression for the derivative of: 2f(x)

A: given that y=2f(x)exdifferentiatee on both side we apply division rulee here

Q: Q3\ Find the derivative of the following function by using the definition f(x) = X-1

A:

Q: Given f(x) : , find f'(-1) using the definition of a derivative. x-2 Provide your answer below: f'(…

A:

Q: Find the absolute maximum and minimum, if either exists, for f(x) = x - 8x + 9. Find the first…

A:

Q: Find the derivative of the function f(x) = 8x2 – 13x by the definition of derivatives f(x + h) –…

A: on using this formula we get = 16x-13

Q: a) Using definition, compute the derivative function of f (x) = 4x7

A: Here, we will find derivative of given function by definition of derivative,

Q: Q1: Using the definition, calculate the derivative of the following function. f(x)=4-x

A:

Q: Let f(x) = }x² – x³. Find the value(s) of x if the second derivative f" (x) equals zero.

A: Use the formula, ddx(xn)=nxn-1 to calculate the derivative. Differentiate f(x) with respect to x to…

Q: Using the definition, caleuhate the derivative of the following function. f (x) = 4-x²

A: Derivative: A function is said to be derivable or differentiable if lim∆x→0fx+∆x-fx∆x exists and…

Q: Find the derivative of all orders of the function. y3D x'-x + 5x-9 y3= %3D

A:

Q: Q2/ Find the derivative of the function f(x) V4-x2 by definition

A: The derivative of a function f(x) with respect to x is given by limh→0fx+h-fxh. The given function…

Q: Given f(x)=√x + 3, find f'(-2) using the definition of a derivative. Provide your answer below: ƒ'(…

A:

Q: function with respect to x. a. f(x) = -4x – 2 b. f(x) = 3x² + 4 c. y = 3x² + 3x + 3

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The first derivative of a continuous function y=f(x) is given, find y’’ and then sketch the general…

A: Our objective is to find y'', and then sketch the general shape of the graph of  f.

Q: Use the Generalized Power Rule to find the derivative of the function. y = (1/w^7-1)^6

A:

Q: Find the derivative of the function f(x) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: Use the first derivative and the second derivative test to determine where each function is…

A: Sketch the function, as follows:

Q: A graph of y f(x) is shown. In the same coordinate system, sketch a graph of the derivative function…

A: In the interval -4,-1, the function is decreasing giving a negative to positive slope.

Q: use the limit process to find the derivative of f(x) = x^3+4x

A: Given,            fx=x3+4x

Q: Find the derivative of the following using the limiting process. f(x)= -4x2 + 5x

A: Given: fx=-4x2+5x

Q: the derivative of the function g(x) In(lx2 +21)

A: We have to find the derivative of g(x)=ln(|x2+2|)

Q: Find the derivative of the function and evaluate f'(x) at the given value of x. f(x)=(3x+1)/(3x-1)…

A: f'(X)= -9/(3x-1)2 f'(3)=-9/64

Q: Use the derivative f'(x) = (x - 3)(x + 4)(x + 4) to determine the maxima and minima of f and the…

A: f will be increasing if f'(x)>0. From the graph of f'(x) we see f'(x)>0 when x>3 [because…

Q: Using the second derivative criterion, find the graphs of the functions b) F(x) = x³/3 - 9x + 3

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Q: Compute the derivative function f' (x) algebraically. f (x) = -5x3 +7 O f' (x) = -15x O f' (x) =…

A:

Q: a) Given f(x) =- 3Vx + 2 Find f'(x) using the definition of derivative.

A:

Q: Q2/ Find the derivative of the function f(x) =V5- x2 by definition

A: →When limit is of the form 00or∞∞ (Indeterminate form ) then L Hospital's rule is used . In this…

Q: A graph of y = f(x) is shown. In the same coordinate system, sketch a graph of the derivative…

A: NOTE: Refresh your page if you can't see any equations. . the given graph is a parabolic graph and…

Q: Assuming g is a differentiable function, find an expression for the derivative of f(x)=(x^2) (g(x)).

A: Assuming g is a differentiable function, find an expression for the derivative of f(x)=(x2) (g(x))

Q: Use the General Power Rule to find the derivative of the function. g(x) = V3 - 9x %3D g'(x) =

A:

Q: 3. If f(x) = 2x² + 3x find f'(a) by using definition of derivative at a point a=4

A:

Q: a) Use the definition of the derivative to find f '(x), given f(x) = 4x² – 1.

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find a function with the given derivative whose graph passes through point P f'(x)=x-4, p(1,7)

A: Integrating on both sides, we get