Questionuation of the line tangent to the graph of at . Next item
Studdy Solution
STEP 1
1. The function given is .
2. We need to find the equation of the tangent line at .
3. The equation of a tangent line can be found using the point-slope form: , where is the slope of the tangent line and is the point of tangency.
STEP 2
1. Find the point of tangency on the curve.
2. Calculate the derivative of the function to find the slope of the tangent line.
3. Use the point-slope form to write the equation of the tangent line.
STEP 3
Find the point of tangency by evaluating the function at :
The point of tangency is .
STEP 4
Calculate the derivative of the function to find the slope of the tangent line. The derivative of is:
Evaluate the derivative at to find the slope :
STEP 5
Use the point-slope form to write the equation of the tangent line. The point-slope form is:
Substitute , , and :
Simplify to get the equation of the tangent line:
The equation of the tangent line is:
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