The tangent line to y=f(x) at (8,0)

Question

passes through the point (7,5). what are f(8) and f'(8)?

Answer 1

The tangent line to the function y = f(x) at (8, 0) that means the function passes through the point (8, 0).

Therefore, f(8) = 0.

The slope (m) of tangent line is first derivative of the given function.

y ' = f ' (x)

m = f ' (x)

Slope of tangent line at (x, y) = (8, 0).

m = f ' (8) --------> equation 1.

Find the slope of tangent line, by using formula : m = [y₂ - y₁ ]/[x₂ - x₁], where (x₁, y₁) and (x₂, y₂) are two points.

Substitute (x₁, y₁) = (8, 0) and (x₂, y₂) = (7, 5) in the above formula.

m = (5 - 0)/(7 - 8)

m = - 5 --------> equation 2.

From equation 1 and 2, f ' (8) = - 5.