Estimate the instantaneous rate of change of the function f(x)=3x^2 + 4x at (1,7)
∆f(x)/∆x = f(x2)-f(x1) / x2-x1
The Attempt at a Solution
I know that x=1 given the point, but to find the instantaneous rate of change I can use x=1.001 as this is a very close number to the point on the tangent curve. So:
∆f(x)/∆x = [3(1.001)^2 + 4(1.001)] - [3(1)^2 + 4(1) ] / 1.001 - 1
= 7.010003 - 7 / 1.001 - 1
The answer in the book is 13 for instantaneous rate of change, and they used the interval 1 ≤ x ≤ 2
I do not understand why they chose to use the point 2, I thought that the point on a tangent must be very close to the x value so wouldn't 1.001 be more appropriate? Have I answered the question correctly? Detailed explanation would be appreciated.