31. Tangent Lines (a) If f(x) = x – 2x + 4, find f'(a). (b) Find equations of the tangent lines to the graph of f at the points whose x-coordinates are 0, 1, and 2. (c) Graph f and the three tangent lines.
Solving:
a) Given:
Take derivative of the given function with respect to x :
Now,
Put x=a:
Hence,
Now,
b) Equation of the tangent line at x-coordinates:
Solution:
Since:
Put x=0:
And,
Hence, The point is : (0, 4) and slope is -2
So, The equation of the tangent line is:
Hence, The equation of the tangent line at (0, 4) is : y+ 2x= 4
Now,
Equation of the tangent line at x=1:
So,
Hence,
To determine the equation of the tangent line at the point (1, 3):
So,
Finding slope :
Hence,
The equation of the tangent line is:
So, The equation of the tangent line at (1, 3) is : y-x= 2
Step by step
Solved in 5 steps with 1 images
