Search any question & find its solution
Question:
Answered & Verified by Expert
The $x$-coordinate changes on the curve $y=3 x^5+15 x-8$ at the rate of $\frac{1}{5}$ units/sec. $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ are the points on the curve at which the $y$-coordinate changes at the rate of 6 units $/ \mathrm{sec}$, then the slope of $A B=$
Options:
Solution:
1524 Upvotes
Verified Answer
The correct answer is:
18
$\begin{aligned} & \text { Given, } y=3 x^5+15 x-8 \\ & \quad \frac{d x}{d t}=\frac{1}{5} \text { unit } / \mathrm{sec} \Rightarrow \frac{d y}{d t}=6 \text { unit } / \mathrm{sec} \\ & \frac{d y}{d t}=\left(15 x^4+15\right) \frac{d x}{d t} \\ & \Rightarrow \quad 6=15\left(x^4+1\right) \times \frac{1}{5} \Rightarrow x^4+1=2 \\ & \Rightarrow \quad x^4=1 \Rightarrow x= \pm 1 \\ & \Rightarrow \quad y(1)=3+15-8=10 \\ & \quad y(-1)=-3-15-8=-26 \\ & \therefore \quad A(1,10), B(-1,-26) \\ & \text { Slope of } A B=\frac{-26-10}{-1-1}=\frac{-36}{-2}=18\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.