Question

a. At what point on the graph y=x⁴ is the slope 256 ? At x= b. What is the second derivative at this point? The second derivative is

Answer 1

The point on the graph y=x⁴ where the slope is 256 is (4, 256). The second derivative at this point is 192.

Step-by-step explanation:

To find the point on the graph y=x⁴ where the slope is 256, we need to find the value of x.

Given the equation y=x⁴, we can find the derivative of y with respect to x, which is 4x³.

Setting 4x³ equal to 256 and solving for x, we get x = 4.

So, the point on the graph y=x⁴ where the slope is 256 is (4, 4^4 = 256).

To find the second derivative at this point, we need to find the derivative of 4x³ with respect to x, which is 12x².

Substituting x = 4, we get the second derivative as 12(4)² = 12(16) = 192.