A function g (x) = 3x^2-5x+4 has graph passing through point P = (a,b) where the line tangent to y = g (x) has slope 12 at point P: Use calculus to find the exact value of a.

Question

A function g (x) = 3x² - 5x + 4 has graph passing through point P = (a,b) where the line tangent to y = g (x) has slope 12 at point P: Use calculus to find the exact value of a.

Answer 1

We need to find out what point on the graph has a slope of 12. To do that, we need to first take the derivative of the function:

g'(x) = 6x - 5

Then we set this equal to 12 to find the x coordinate:

6x - 5 = 12

6x = 17

x = 17/6

Since the question only asks for the x-coordinate, we are done. a = 17/6.