Question

Find the slope, m, of the tangent to the curve y = 4 - 5x² - 2x³ at the point where x = a.

Answer 1

To find the slope, m, of the tangent to the curve y = 4 - 5x² - 2x³ at the point where x = a, differentiate the function and substitute x = a into the derivative to find the slope.

Step-by-step explanation:

To find the slope, m, of the tangent to the curve y = 4 - 5x² - 2x³ at the point where x = a, we need to find the derivative of the function and then substitute the value of x = a into the derivative.

1. First, find the derivative of the function y = 4 - 5x² - 2x³. Differentiate each term with respect to x using the power rule.
2. Next, substitute x = a into the derivative to find the slope at the point.
3. Simplify the expression to get the final answer for the slope, m.

Therefore, the slope of the tangent to the curve is m = -20a² - 10a.