I need help on my math portfolio. Here's the intro:
An estimate for the slope of a tangent to the graph of a non-linear function, f(x), at a point on the graph where x=a can be obtained using a small value of h and evaluating the function at the points x=a+h and x=a-h to obtain f(x+h) and f(x-h) then using the formula: (f(a+h) - f(a-h)) / 2h
This formula will give a good estimate of the slope of the tangent to the function at the point x=a. Using successively smaller values for h will give progressively better results.
1. Use the function f(x) = x^3 to estimate the slope of the tangent to the function at x =2. Evaluate ((2+h)^3 - (2-h)^3) / 2h for h=1, h=0.1, h=0.01 and h=0.001. Use your results to make a prediction of the exact value of the slope of f(x) = x^3 at x=2. Justify your answer. PLEASE SHOW ALL WORD YOU USED AND EXPLAIN!
2. Use your calculator to repeat the exploration of the slope of f(x) = x^3 at the points x =1,3,4,5.
3. a) There is a simple function of x, which gives the value of the slope of f(x) = x^3 for any value of x. Find it.
b) Predict the slope of the tangent at x= -1 and x=6 using the function you just found.
c) Test your prediction with your calculator.
4. Use the same steps from questions 2,3, and 4 to explore the slope of f(x) = x^4
I REALLY NEED YOUR HELP MATH EXPERTS!! PLEASE SHOW ME WHAT TO DO!!
An estimate for the slope of a tangent to the graph of a non-linear function, f(x), at a point on the graph where x=a can be obtained using a small value of h and evaluating the function at the points x=a+h and x=a-h to obtain f(x+h) and f(x-h) then using the formula: (f(a+h) - f(a-h)) / 2h
This formula will give a good estimate of the slope of the tangent to the function at the point x=a. Using successively smaller values for h will give progressively better results.
1. Use the function f(x) = x^3 to estimate the slope of the tangent to the function at x =2. Evaluate ((2+h)^3 - (2-h)^3) / 2h for h=1, h=0.1, h=0.01 and h=0.001. Use your results to make a prediction of the exact value of the slope of f(x) = x^3 at x=2. Justify your answer. PLEASE SHOW ALL WORD YOU USED AND EXPLAIN!
2. Use your calculator to repeat the exploration of the slope of f(x) = x^3 at the points x =1,3,4,5.
3. a) There is a simple function of x, which gives the value of the slope of f(x) = x^3 for any value of x. Find it.
b) Predict the slope of the tangent at x= -1 and x=6 using the function you just found.
c) Test your prediction with your calculator.
4. Use the same steps from questions 2,3, and 4 to explore the slope of f(x) = x^4
I REALLY NEED YOUR HELP MATH EXPERTS!! PLEASE SHOW ME WHAT TO DO!!