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Sagot :
Answer:
[tex]y - 20 = 24(x - 3)[/tex]
Step-by-step explanation:
Equation of a line:
The equation of a line, in point-slope form, has the following format:
[tex]y - y_0 = m(x - x_0)[/tex]
In which the point is [tex](x_0,y_0)[/tex] and the slope is m.
(3, 20)
This means that [tex]x_0 = 3, y_0 = 20[/tex]. So
[tex]y - y_0 = m(x - x_0)[/tex]
[tex]y - 20 = m(x - 3)[/tex]
Slope:
The slope is the derivative of the function at the point:
The function is:
[tex]y = x^3 - 3x + 2[/tex]
The derivative is:
[tex]y^{\prime}(x) = 3x^2 - 3[/tex]
At the point, we have that [tex]x = 3[/tex]. So
[tex]m = y^{\prime}(3) = 3*3^2 - 3 = 27 - 3 = 24[/tex]
So the equation to the tangent line to the curve a the point is:
[tex]y - 20 = 24(x - 3)[/tex]
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