Question

For which of the values of x, the rate of increase of the function y=3x^2-2x+7 is 4 times the rate of increase of x?

(a) -1

(b) \(\frac{1}{3}\)

(c) 1

(d) 0

The question was posed to me by my college director while I was bunking the class.

The origin of the question is Derivatives Application in portion Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (c) 1

The best I can explain: Given that, \(\frac{dy}{dt}=4.\frac{dx}{dt}\)

y=3x^2-2x+7

\(\frac{dy}{dt}\)=(6x-2) \(\frac{dx}{dt}\)

4.\(\frac{dx}{dt}\)=(6x-2) \(\frac{dx}{dt}\)

4=6x-2

6x=6

⇒x=1