Answer:
y = 4x + 9/4
Step-by-step explanation:
4x − y − 3 = 0
y = 4x − 3
The slope of the line is 4.
The slope of the tangent line is:
f(x) = x − x²
f'(x) = 1 − 2x
Setting the slope equal to 4:
4 = 1 − 2x
2x = -3
x = -3/2
The point on f(x) is:
f(-3/2) = -3/2 − (-3/2)²
f(-3/2) = -3/2 − 9/4
f(-3/2) = -15/4
Using point-slope form:
y − (-15/4) = 4 (x − (-3/2))
y + 15/4 = 4 (x + 3/2)
y + 15/4 = 4x + 6
y = 4x + 9/4
