write an equation for the line tangent to the graph of f at (-1,3/2) and use it to approximate f(-1,1)
To write an equation for the tangent line to the graph of function f at the point (-1, 3/2), we need to find the slope of the tangent line at that point first.
The slope of the tangent line can be obtained using the derivative of the function. So, the first step is to find the derivative of function f.
Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line. Finally, we can use this equation to approximate the value of f(-1, 1).
Let's walk through the steps:
Step 1: Find the derivative of function f
Differentiate function f to obtain its derivative, f'(x). The derivative represents the slope of the tangent line at any given point on the graph of f.
Step 2: Find the slope at the given point (-1, 3/2)
Evaluate the derivative, f'(-1), at x = -1 to find the slope of the tangent line at that point. This will be the slope of the desired tangent line.
Step 3: Write the equation of the tangent line using the point-slope form
Now that we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.
Substitute the point (-1, 3/2) and the slope obtained in step 2 into the point-slope form equation to get the equation of the tangent line.
Step 4: Use the equation to approximate f(-1, 1)
Substitute x = -1 into the equation obtained in step 3 to approximate the value of f(-1, 1).
By following these steps, you should be able to find the equation of the tangent line at (-1, 3/2) and use it to approximate f(-1, 1).