Tutorial Exercise Write the equation of the tangent line to the curve at the indicated point....

Transcribed Image Text:

Tutorial Exercise Write the equation of the tangent line to the curve at the indicated point. As a check, graph both the function and the tangent line. x5 5 f(x) = = at x = -1 5 x5 Step 1 We want to find the equation of the tangent line to the curve given by f(x) = point on the line. x5 5 5 X at x=-1. We need to find two things to get the equation of the line: the ---Select--- of the line an Beginning with the slope, we know that the slope of a tangent line to a curve is given by the derivative of the function. To find the derivative of f(x), we first rewrite it so that each term is a x5 power of x. This gives f(x) - 5x So the derivative is given by Submit f'(x)=5 = 5 4-5 ( Skip (you cannot come back) Tutorial Exercise Write the equation of the tangent line to the curve at the indicated point. As a check, graph both the function and the tangent line. x5 5 f(x) = = at x = -1 5 x5 Step 1 We want to find the equation of the tangent line to the curve given by f(x) = point on the line. x5 5 5 X at x=-1. We need to find two things to get the equation of the line: the ---Select--- of the line an Beginning with the slope, we know that the slope of a tangent line to a curve is given by the derivative of the function. To find the derivative of f(x), we first rewrite it so that each term is a x5 power of x. This gives f(x) - 5x So the derivative is given by Submit f'(x)=5 = 5 4-5 ( Skip (you cannot come back)