Find the function g(z) satisfying the two conditions: 1. g'(x) = -4096 - 1³ 2. The maximum value of g(x) is 7. g(x) =

Q: Find the relative extrema of f(x) = (x4 + 1)/x2 .

A: Given: f(x) = (x4 + 1)/x2  To Find: Relative extrema of f(x).   Concept: First-Derivative Test:

Q: Find f-1(x) f(x)=(e-x)/x

A: Given, f(x)=(e-x)/x To find f-1(x)

Q: Find f (x) if f'(x) = 3x² + 4x + 1 and f (2) = 21. f (x)

A:

Q: f(x)=1/x+7 f-1(x)=

A: Given function is

Q: Find g(x) if g'(x) = (60x² 80x) g(x) = 4x 4 - 8x and g(0) = 3.

A: Giveng'(x)=(60x2-80x).44x3-8x2  and g(0)=3

Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Let f(6) = 54 and f'(6) = 19. Let g(x) = (13+x²)f(x). Calculate the value of g' (6). %3D

A:

Q: AB1: Find g(2), g'(2), and g"(2).

A: Given that gx=∫-2x2ftdt Now we have to find g2, g'2 and g''2 In the interval -2,2, fx=4-x2In the…

Q: f(x) = In(5 + 4x)

A: Given: - The function is, f(x)=ln(5+4x) To find: - The derivative of the given function.

Q: Verify that f′(x) = g′(x) and explain the relationship between f and g

A: fx=3xx+2f'x=ddx3xx+2=x+2(3)-(3x)(1)x+22=3x+6-3xx+22=6x+22

Q: a) Differentiate the function Q(p) = -2√/p³ (e-P-PB). b) Hence or otherwise, determine Q'(1).

A: The given function .The aim is to find the derivative function  and find the value of .

Q: Find (f ¹)'(a). f(x) = √ 3x³ + 3x² + 2x + 1, (f−¹)'(a) = X a = 3

A:

Q: f(x)=x2(6+x)5. ​Find f′(x)using the Quotient Rule and the Extended Power Rule.

A:

Q: For the function f(x) = -2ex, find f''(x), f''(0), f''(7), and f''(-9).

A: Solution :-

Q: 5 Find f such that f'(x) = - √x f(16) = 49.

A: f′(x)=5x,f(16)=49

Q: Differentiate the function and simplify the answer. f(x) = 2x e2r'+x² Select one: f'(x) = 2xe2r³+x?…

A:

Q: 1 For the function f (x) = 2 (x + 4) – 6, find f(x).

A:

Q: Let g(x) = x³ – 6x + 8. Find f(x) so that f'(x) = g'(x) and ƒ(1) = 1. NOTE: Enter the exact answer.…

A: