Question
Mathematics Question on Applications of Derivatives
If f (x) = 3x2+15x+5, then the approximate value of f (3.02) is
A
47.66
B
57.66
C
67.66
D
77.66
Answer
77.66
Explanation
Solution
Let x = 3 and ∆x = 0.02. Then, we have
f(3.02)=f(x+Δx)=3(x+Δx)2+15(x+Δx)+5
Now,Δy=f(x+Δx)-f(x)
=f(x-Δx)=f(x)+Δy
≈f(x)+f'(x)Δx (As dx=Δx)
f(3.02)=(3x2+15x+5)+(6x+15Δx)
77.66
Hence, the approximate value of f(3.02) is 77.66.
The correct answer is D.