Question

Help find the equation of the tangent line please (calculus)

Answer 1

The tangent line to f(x) at x = c has slope equal to the derivative at c, or f'(c).

We have

f(x) = 3 - 2 x + 7 x²

so that

f'(x) = -2 + 14 x

The slope is 5 for

-2 + 14 x = 5 ==> 14 x = 7 ==> x = 1/2

Now, f (1/2) = 15/4, so the tangent line has equation

y - 15/4 = 5 (x - 1/2) ==> y = 5 x + 5/4