UGRD-MATH6100 Calculus 1

Question

Let f(x) = -x⁴-x-1, evaluate f(-1) and -2f(1). Tangent line velocities growth

Answer 1

f(x)= -x^4 -x -1

f(-1)=-1+1-1 =-1

-2f(1)= -2(-1-1-1)= -2(-3)= 6

tangent lines have slopes = derivative=f'(x)

f'(x)=-4x^3 -1

f'(-1) = 3

f'(1) = -5

-2f'(1)= 10

slope of the tangent line grew by 7 from 3 to 10, or about 233%

slope is a rate of change like velocity