Question

Maximum Slope of Curve : \(-x^3 + 6x^2 + 2x + 1\) is:

Answer 1

find the max of the derivative
the derivative is a quadratic, and the max is the second coordinate of the vertex

Answer 2

The derivative is :

\[-3x^2 + 12x + 2 = 0\]

Answer 3

Solving this :

I got 4.16 and -0.16 something..

Answer 4

I am not getting properly @satellite73

Answer 5

Satellite is correct: we solve this problem by finding the maximum value of the derivative of the given function. You've found the derivative of the given function correctly: It's -3x^2 + 12x + 2.
Now start all over. Given the (new) function y=-3x^2 + 12x +2, maximize it.
This means you must again differentiate, and must set the resulting derivative = to 0 (do NOT set -3x^2+12x+2= to 0 as you did earlier). Try again?

Answer 6

do not set the derivative equal to zero

Answer 7

For reference: the slope of the original function is a maximum when x=2. Can you find that maximum slope, using this fact?

Depends upon which derivative we're talking about! You took the original function, found its derivative, and set that derivative = to 0. This is incorrect in this particular problem.

Please go back to my previous comments and see if you can follow the procedure I've suggested.

Answer 8

the derivative is a function
\[f'(x)=-3x^2 + 12x + 2 \] not an equation
find the vertex of this parabola
first coordinate of the vertex is \(-\frac{b}{2a}=2\)

Answer 9

the second coordinate of the vertex is its maximum, which is
\[f'(2)\] whatever that is

Answer 10

I got it Satellite..

ExperimentX told be on facebook just now.

We have to take derivative again and then x = 2 will be maxima..

Answer 11

By putting x(2) in f'(x) I got 14.. Thank you..

Answer 12

yw

Answer 13

The slope of the original function is y'=-3x^2 + 12x +2. You found that the critical value of this slope function is 2. Merely substitute 2 into y'(x) = -3x^2 + 12x + 2 to determine the maximum slope of the original function. Yes, 14.

One comment: You typed, "then x=2" will be maxima." What you mean here is that "the slope of the original function has its maximum value AT x= 2."