find an equation for the line tangent y= -5 - 4x^2 at (-3, -41)

Answer 1

The slope of the tangent line to a function can be found by taking the derivative of that function.

For y = -5 - 4x², the derivative (y') is found using the power rule:

y' = -8x

For the point (-3, -41), x = -3 so the slope is -8(-3) = 24

You can now use the point-slope form of a line y - y₁ = m(x - x₁) where (x1, y1) is (-3, -41) and m = 24:

y - -41 = 24(x - -3)

y + 41 = 24(x + 3)

If you'd like, you can leave it like this or put it into the slope-intercept form:

y = 24x +31