Answer to Question #167025 in Calculus for Samir khan

Question

Determine all of the points on the curve

y = 3x2 + 24x - 3 where the slope of the tangent line is 6

Answer 1

Consider the function $y=3x^2+24x-3$

Differentiate the function $y$ with respect to $x$ as,

$\frac{dy}{dx}=\frac{d}{dx}(3x^2+24x-3)$

$=3(2x)+24(1)$

$=6x+24$

Since, the slope of the tangent line is $6$ , therefore,

$\frac{dy}{dx}=6$

$6x+24=6$

$6x+24-24=6-24$

$6x=-18$

$x=-3$

At $x=-3$ , $y=3(-3)^2+24(-3)-3=-48$

Therefore, the point on the curve in ordered pair is $(-3,-48)$.