Find an equation of the tangent line to y=x^4 - x^3 at (-1,2)

Question

Find an equation of the tangent line to y=x⁴ - x³ at (-1,2)

Answer 1

All lines have the form y = mx + b where m is the slope of the line and b is the y-intercept. So we need to find the values of m and b for line tangent to y = x⁴ - x³ at the point (-1,2). The slope is easy - it's the value of the derivative at x = -1:

m = dy/dx = 4x³ - 3x² = 4(-1)³ - 3(-1)² = -4 -3 = -7

So the equation of the tangent line so far is y = -7x + b. To find the value of b, plug in the given point (-1,2) and solve for b:

y = -7x + b

2 = 7(-1) + b

Solve for b.