Question

For the function f, f'(x)= 2x+1 and f(1)=4. What is the approximation for f(1.2) found by using the line tangent to the graph of f at x=1?

Answer 1

L(x) = f(a) + f'(a)(x - a)
L(1.2) = f(1) + f'(1)(1.2 - 1) = 4 + (2(1) + 1)(0.2) = 4 + 3(0.2) = 4 + 0.6 = 4.6