Question

17. What is the simplified average rate of change between x = 2 and x = 2 + h for the function: ƒ(x) = x² - 3x?

18. Based on your result from above, what is the slope of the tangent to f(x) at the point when x = 2?

19. Find the slope of the tangent line to f(x) = 2x⁴ +1   when  x = 2 using first principles.

20. Use your answer from 19) to determine the equation (in the form of y=mx+b) of the tangent line to f(x) at x=2.

16. Determine the limit by showing all your steps, if it exists. limx→255−x√25−x

15. Find the point(as an ordered pair) on the curve  f(x)=−4x^2−3 at which there exists a tangent with slope of 4. Show your work using first principles.

14. Determine the slope of the tangent to the curve y=3x^3+4x  at the point   ( 1 , 7 ) using first principles.

13. The population growth P(t) in a community is projected to follow the function

P= 7t² + 5t + 350 , where t is time in years. Estimate the instantaneous rate of growth in the 5^th year by showing all of your steps on paper.

12. The population growth, P(t) in a community is projected to follow the function

P(t) = 7t² + 5t + 350, where t is time in years. Find the average rate of growth from the 2^nd to the 5^th year.

11. What happens when a limit does not equal the same value from the left and the right, such as:limx→3+f(x) = −4limx→3−f(x) = 2?

Answer 1