Question

Use the definition

mₜₐₙ=(f(a+h)-f(a))/{h} to find the slope of the line tangent to the graph of f at P.
b. Determine an equation of the tangent line at P.
f(x) = x²-9, P(-5,16)

Answer 1

The slope of the line tangent to the graph of f at P is mₜₐₙ = h + 10.

Step-by-step explanation:

To find the slope of the line tangent to the graph of f at P, we can use the formula mₜₐₙ=(f(a+h)-f(a))/{h}.

Given that f(x) = x²-9 and P(-5,16), we can substitute the values into the formula to find the slope.

Substituting the values, we get mₜₐₙ = (f(-5+h) - f(-5))/h = ((-5+h)² - (-5)²)/h = (h² + 10h)/h = h + 10.

Therefore, the slope of the line tangent to the graph of f at P is mₜₐₙ = h + 10.