Calculus

Correct. This question involves using the power rule for differenti find g'x=4x3-9x2-1 and then solving an equation. The c 4x3-9x2-1= 1/2 .

Let y be defined implicitly by the equation 4x+frac 2y3=75. Use implicit differentiation to find dy/dx .

Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. fx=ln 5x2+1

Find and describe all of the solution curves to the differential equation [f't]2= 4ft . Hint: There are infinitely many different solutions which satisfy f0=0.

Find the derivative of the function. fx=frac x+ square root of 3x3x-5 f'x=square ×

The top of a 25-foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute. When the top of the ladder is 7 feet from the ground, what is the rate of change of the distance between the bottom of the ladder and the wall?

Determine whether Rolle's Theorem applies to the function fx=-x2+8x-1 on the interval [3,5] . If it applies, find all possible values of e as in the conclusion of the theorem. Separate multiple answers with a comma. If the theorem does not apply, write NA for your answer.

Which of the following is d/dx 4tan -13x 2 Select the correct choice below. A. frac 121+9x2 B. frac 11+9x2 C. -frac 11+9x2 D. -frac 121+9x2

Find the value or values of c that satisfy the equation frac fb-fab-a=f'c in the conclusion of the mean value theorem for the function and interval shown below. fx=ln x-1,[2,4] c=frac 2ln 5+1 Type an exact answer. Use a comma to separate answers as needed.

A relative maximum is the same as an absolute maximum. True False