calculus Question

Question

At what point is the tangent to the curve defined by the function f(x) = 4x²-x+5 parallel to the line y-15x=1?

 

Help!

Answer 1

y - 15x = 1

y = 15x + 1

So the slope we need is m=15.

 

 f'(x) = 8x - 1.

 If 8x-1 = 15, then 8x = 16, so x=2.

 

Finally f(2) = 16 - 2 + 5 = 19

 

So at the point (2,19) is where f(x) is tangent to the line y = 15x + 1