Question

Find the equation of all the lines having slope 0 which are tangent to the curve y=6x^2-7x.

(a) \(\frac{24}{49}\)

(b) –\(\frac{24}{49}\)

(c) \(\frac{49}{24}\)

(d) –\(\frac{49}{24}\)

This question was addressed to me during an interview for a job.

This intriguing question originated from Derivatives Application in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Right answer is (d) –\(\frac{49}{24}\)

Explanation: Given that, y=6x^2-7x

\(\frac{dy}{dx}\)=12x-7

It is given that the slope of tangent is 0

∴12x-7=0

⇒x=\(\frac{7}{12}\)

∴ y]x=\(\frac{7}{12}\)=6(\(\frac{7}{12}\))^2-7(\(\frac{7}{12}\))

6(\(\frac{49}{144})-\frac{49}{12}=49(-\frac{1}{24})=-\frac{49}{24}\)