The local maximum value of the function is 1.24.
The curve of a function has peaks and troughs called maxima and minima. A function may have any number of maxima and minima. Calculus allows us to determine any function's maximum and lowest values without ever consulting the function's graph.
Given function as :
g(x) = x³ + 5x² - 17x - 21
Differentiated with respect to x
g'(x) = 3x² + 5(2x) - 17(1)
g'(x) = 3x² + 10x - 17
Now g'(x) = 0
So, 3x² + 10x - 17 = 0
x = ( -5±2√19)/3
x = 1.239, x = - 4.5725
So, the local maxima = 1.239 = 1.24 (the nearest thousandth)
Hence, the local maximum value of the function is 1.24.
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