The equation of the tangent line at the point is y = 9/2x - 3
How to determine the equation of the tangent line
From the question, we have the following parameters that can be used in our computation:
f(x) = −7x² + 9/2x − 3
Also, we have
x = 0
Calculate f(0)
f(0) = −7(0)² + 9/2(0) − 3
f(0) = -3
Differentiate the function to calculate the slope m
So, we have
m = -14x + 9/2
Set x = 0
m = -14(0) + 9/2
m = 9/2
The equation of the tangent line is then calculated as
y = m(x - X) + f(X)
So, we have
y = m(x - 0) + f(0)
This gives
y = 9/2(x - 0) - 3
Expand
y = 9/2x - 3
Hence, the equation is y = 9/2x - 3