Answer to Question #268654 in Calculus for Jess

Question

A function is given by the equation 𝑦 = 2𝑥 3 + 4𝑥 2 − 5𝑥 + 10.

i) Obtain an expression for 𝑑𝑦 𝑑𝑥.

ii) Find the gradient of the tangent to the curve at (2, 6).

iii) Determine the equation of this tangent line which passes through (2, 6)

Answer 1

$y=2x³+4x²-5x+10$

(i) $\frac{dy}{dx}=6x²+8x-5$

(ii) gradient at (2, 6)

$=> x=2, y = 6$

$\frac{dy}{dx}=6x²+8x-5=6(2)²+8(2)-5=35$

(iii) $\frac{dy}{dx}=m=\frac{y-y_1}{x-x_1}$

$=> 35=\frac{y-6}{x-2}$

$=> 35(x-2)=(y-6)$

$=>35x-70=y-6$

$=> y-35x+64=0$