Question

For the function, f(t)=1/a(9 t³-71 t²+213)⁴5, find the value of a that would make the slope of the tangent line -180 at t=2. a=__

Answer 1

To find the value of a that would make the slope of the tangent line -180 at t=2, take the derivative of the function and substitute t=2 into it. Solve the resulting equation to find the value of a.

Step-by-step explanation:

To find the value of a that would make the slope of the tangent line -180 at t=2, we can use the formula for the derivative of the function.

First, we need to find the derivative of the function f(t)=1/a(9t³-71t²+213)⁴5. Taking the derivative, we get f'(t) = 1/a(36t² - 142t + 213)⁴⁴5.

Now, we can substitute t=2 into the derivative and set it equal to -180:
-180 = 1/a(36(2)² - 142(2) + 213)⁴⁴5

By solving this equation for a, we can find the value that would make the slope of the tangent line -180 at t=2.