Question

Let f and g be twice differentiable functions on R such that
f''(x)=g''(x)+6x
f''(1)=4g'(1)-3=9
f(2)=3g(2)=12.
Then which of the following is NOT true?

• A. If $−1<𝑥<2$, then $|𝑓(𝑥)−𝑔(𝑥)|<8$
• B. $|𝑓'(𝑥)−𝑔'(𝑥)|<6⇒−1<𝑥<1$
• C. $𝑔(−2)−𝑓(−2)=20$
• D. There exists $𝑥_0∈(1,\frac{3}{2})$ such that $𝑓(𝑥0)=𝑔(𝑥0)$

Answer 1

Answer: (A)

If $−1<𝑥<2$, then $|𝑓(𝑥)−𝑔(𝑥)|<8$

Answer 2

The Correct option is (A): If $−1<𝑥<2$, then $|𝑓(𝑥)−𝑔(𝑥)|<8$