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2 answers:
Hey there! :)
Answer:
2nd option: (4, -136) is a relative minimum, (-2, 80) is a relative maximum.
Step-by-step explanation:
To begin, we can graph this equation (pictured on bottom of answer)
Relative minimums/maximums are the minimums and maximums of turning points of the graph. Observing the graph, we can see that:
(-2, 80) is a relative maximum because this is the maximum value at a turning point.
(4, -136) is a relative minimum because this is the minimum value at a turning point.
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The derivative of the function at this point is negative, which tells us <em>the function is decreasing at that point</em>.
The tangent to the line is a straight line, so we will have a linear equation of the form y = mx + c. We know the gradient, m, is equal to -1, so
Now we need to substitute a point on the tangent into this equation to find c. We know a point when x = 0 lies on here. To find the y-coordinate of this point we need to evaluate f(0).
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