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The volume of a cone uses the following formula:
Our diameter is 20 feet, so divide this by 2 to find the radius:
We now have all of our values need to fill in the formula. Plug in these values:
The volume of the cone is 1780 cubic feet.
Our diameter is 20 feet, so divide this by 2 to find the radius:
We now have all of our values need to fill in the formula. Plug in these values:
The volume of the cone is 1780 cubic feet.
Explanation
We must the tangent line at x = 3 of the function:
The tangent line is given by:
Where:
• m is the slope of the tangent line of f(x) at x = h,
,• k = f(h) is the value of the function at x = h.
In this case, we have h = 3.
1) First, we compute the derivative of f(x):
2) By evaluating the result of f'(x) at x = h = 3, we get:
3) The value of k is:
4) Replacing the values of m, h and k in the general equation of the tangent line, we get:
Plotting the function f(x) and the tangent line we verify that our result is correct:
AnswerThe equation of the tangent line to f(x) and x = 3 is: