SOLUTION: At what values of x on the curve y=5+40x^3-3x^5 does the tangent line have the largest slope?

Question 1180886: At what values of x on the curve y=5+40x^3-3x^5 does the tangent line have the largest slope?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

At what values of on the curve
does the tangent line have the largest slope?

To find where the slope of the tangent line is the largest, we need to find the inflection points which occur when the second derivative equals zero:

solutions:
=>
=>
=>
=>

The roots to the above equation are
, ,
however, we must check each one to see what the slope is at these points.

At , we have

.
At , we have

At , we have

Therefore, the tangent line to the curve has the largest slope at
and
and the value of the largest slope is at these points.

RELATED QUESTIONS
At what value(s) of x on the curve y=−9+250x 3 −3x 5 does the tangent line (answered by KMST)

Find the minimum slope of the line tangent to the curve y = x�-3x�+6x+3. (answered by Boreal)

Find the minimum slope of the line tangent to the curve y =... (answered by KMST)

What is the slope of the tangent line to the curve y = 2x^4 + x^3 + 6x at x =... (answered by Alan3354)

what the slope of the tangent line of the curve x^2-xy+y^2=3 at a point... (answered by ikleyn)

Consider the curve with equation y^2 = x^3 + 3x^2. a. Find an equation of the tangent... (answered by Fombitz)

What is the equation of the tangent line to y=x^2+2x-3 at (1,0)? At what value of... (answered by Fombitz)

Let f(x)=4-x^2. The equation of the tangent line to the curve at (1,3) is 2x+y=5. a. (answered by Solver92311)

Let f(x)=4-x^2. The equation of the tangent line to the curve at (1,3) is 2x+y=5. a. (answered by Solver92311,Alan3354)