Help with calculus please!

Question

Find the equation of the line tangent to y = 2x² - x + 4 at x = 3.

Question options:

1)	y = 11x - 14
2)	y = 4x + 14
3)	y = 4x + 3
4)	y = 11x + 3

Answer 1

To find the equation of the tangent line, you first find the slope of the line at the given point (x=3).

To do this, take the derivative and plug in 3:

f'(x)=4x-1 so f'(3)=11

You then plug this slope into the formula for a line, which is:

Y2-Y1= slope(x2-x1) where x1 and y1 represent any point along the line. We have an x value, we have the slope, so now we just need a corresponding y value. Plug 3 into the original equation and you'll get 19. So the equation is:

Y-19= 11(x-3)

Simplify:

Y-19=11x-33

Y=11x-14

The Answer is A