If f (3) = 9 and f ´(3) = 4, find the tangent line to the graph of f when x = 3
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No, do not do hat.
slope m = 4
9 = 4(3) + b
b = -3
so
y = 4 x - 3
To find the equation of the tangent line to the graph of f when x = 3, you need to use the point-slope form of a linear equation. This form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a known point on the line, and m is the slope of the line.
In this case, the point (x₁, y₁) is (3, f(3)) = (3, 9), and the slope m is given by f'(3) = 4.
Using these values, we can substitute them into the point-slope form:
y - 9 = 4(x - 3)
Now, simplify and rewrite the equation in the slope-intercept form (y = mx + b), where b is the y-intercept:
y - 9 = 4x - 12
y = 4x - 3
So, the equation of the tangent line to the graph of f when x = 3 is y = 4x - 3.