Question

Find the equation of the tangent to the curve $y=-5x^2+6x+7$ at the point $(1/2,35/4)$.

• A. $y=x+\frac{33}{4}$
• B. $y=x-\frac{33}{4}$
• C. $y=\frac{33}{4}x$
• D. none of these

Answer 1

The correct option is A $y=x+\frac{33}{4}$

The equation of the given curve is $y=-5x^2+6x+7$

$\frac{dy}{dx}=-10x+6$

${\left(\frac{dy}{dx}\right)}_{1/2,35/4}=-\frac{10}{2}+6=1$

The required equation of the tangent at $(1/2,35/4)$ is :

$y-\frac{35}{4}={\left(\frac{dy}{dx}\right)}_{1/2,35/4}(x-\frac{1}{2})$

$y-\frac{35}{4}=1(x-\frac{1}{2})$

$y=x+\frac{33}{4}$