Question #072cb
2 Answers
To find the slope, evaluate
Explanation:
The equation for the slope of the tangent line is:
We can find local maxima by computing the next derivative, setting that equal to 0, and then solving for the value(s) of x.
Compute the next derivative:
Set it equal to 0:
20x^3+ 6x = 0#
Factor:
Discard the imaginary roots.
Compute the next derivative:
Evaluate it at
To find the slope, evaluate
Explanation:
The tangent line will be the derivative of the function.
To find the minimum value of this line we have to find the critical points. So we find the second derivative
The minimum will be when this function is equal to zero
From this we can see that either factor will only be equal to zero when
So we plug this into the tangent line formula to get the slope at this point.