Question

Find the slope, m, of the tangent to the curve y = 75x² - 2x³ at the point where x = a.

Answer 1

The slope of the tangent to the curve y = 75x² - 2x³ at the point where x = a is 150a - 6a².

Step-by-step explanation:

To find the slope of the tangent to the curve y = 75x² - 2x³ at the point where x = a, we need to find the derivative of the function and evaluate it at x = a. The derivative of y with respect to x is dy/dx = 150x - 6x². Substituting x = a into the derivative, we have dy/dx = 150a - 6a². Therefore, the slope of the tangent at x = a is 150a - 6a².