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Given x = 3t² + 1 and y = t³ + 6t + 2. Find (dy)/(dx) at t=1.

April 8, 2026Mathematics

ScanSolve AI Answer

Graph of y = t³ + 6t + 2

Key points of y = t³ + 6t + 2
Point	t	y
x-intercept	−0.33	0
y-intercept	0	2

Step-by-step solution

2 steps

Here are the solutions to the questions in Section A:

Question 1:
Given $x = 3t^2 + 1$ and $y = t^3 + 6t + 2$ . Find $\frac{dy}{dx}$ at $t=1$ .

Differentiate $x$ with respect to $t$ .
$\frac{dx}{dt} = \frac{d}{dt}(3t^2 + 1) = 6t$
Differentiate $y$ with respect to $t$ .
$\frac{dy}{dt} = \frac{d}{dt}(t^3 + 6t + 2) = 3t^2 + 6$
Step

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