Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. f(x) = −7x2 + 10x

Answer 1

f(x) = -7x² + 10x

f(x+h) = -7(x+h)² + 10(x+h) = -7(x² + 2xh + h²) + 10x + 10h

f(x+h) - f(x) = -14xh - 7h² + 10h

[f(x+h) - f(x)] / h = -14x - 7h + 10

f'(x) = lim_h→0[(f(x+h) - f(x)) / h] = lim_h→0(-14x - 7h + 10) = -14x + 10

Answer 2

y = f(x) = -7x^2+10x

Differentiating via power rule:

y ' = -14x + 10 = f'(x)

There ya go