Question

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

Answer 1

Answer:

$11x - y + 3.25 = 0$

Step-by-step explanation:

Let the equation be a function of x,

$f(x) = 5x^2 + 6x + 7$

Calculating its derivative,

$f'(x) = 10x + 6$

Now, this function returns the slope of the tangent line for given value of x. We are given the point ( 0.5 , 35/4 ). So, substitute x=0.5 in the above function.

$f'( 0.5 ) = 10( 0.5 ) + 6 = 11$

The slope of the tangent line is 11 which passes through a given point. Use slope-point form of line,

$y - \frac{35}{4} = 11( x - 0.5 )\\y - 8.75 = 11x - 5.5\\11x - y = -3.25\\11x - y + 3.25 = 0$

Thats the equation of the line.