To find the point on the curve where the tangent has an inclination of 45°, we need to find the derivative of the curve and set it equal to the tangent's slope, which is the tangent of 45°.
First, let's find the derivative of the curve by differentiating each term:
y = 7x - 3x² + 2
dy/dx = d(7x)/dx - d(3x²)/dx + d(2)/dx
= 7 - 6x
Now we set this derivative equal to the tangent of 45°:
7 - 6x = tan(45°)
Since the tangent of 45° is equal to 1, we can simplify this equation:
7 - 6x = 1
Next, we solve for x:
-6x = 1 - 7
-6x = -6
x = 1
Now that we have the value of x, we can substitute it back into the original equation to find the value of y:
y = 7(1) - 3(1)² + 2
= 7 - 3 + 2
= 6
Therefore, the point on the curve where the tangent has an inclination of 45° is (1, 6).
Find the point on the curve y = 7x-3x² + 2 where the inclination of the
tangent is 45°.
1 answer