The equation of a line that is tangent to the graph of f and parallel to the given line is; y = 3x + 2 and y = 3x - 2
How to find the equation of a line in slope intercept form
The given equation of the line is 3x - y + 3 = 0
In slope intercept form, this can be rewritten as;
y = 3x + 3
Therefore, the slope of this line will be 3 since in y = mx + c, m is the slope. Thus, the slope of the parallel line will be 3
We will be looking for the value of x when the derivative of f(x) equals 3.
f(x) = x³ and so f'(x) = 3x²
Thus;
3x² = 3
x² = 3/3
x² = 1
x = 1 or -1
Thus;
y = 1³ or y =-1³
y = 1 or -1
Equation of tangent is;
y - 1 = 3(x - 1)
y - 1 = 3x - 3
y = 3x - 2
or y - (-1) = 3(x - (-1))
y + 1 = 3x + 3
y = 3x + 2
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