it's urgent plzzz solve question number 22.
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22. y = 2x + 3x² - x³ -27
differentiate with respect to x
dy/dx = 2 + 6x - 3x²
Let dy/dx = g(x)
g(x) = 2 + 6x - 3x²
dy/dx = g(x) is the slope of function y
diffentiate g(x) with respect to x
dg(x)/dx = 6 - 6x = 0
x = 1
again, differentaite with respect to x
d²g(x)/dx² = -6 < 0
hence, g(x) is maximum at x = 1
now,
maximum slope = 2 + 6x - 3x² at x = 1
= 2 + 6(1) -3(1)²
= 2 + 6 - 3
= 5
differentiate with respect to x
dy/dx = 2 + 6x - 3x²
Let dy/dx = g(x)
g(x) = 2 + 6x - 3x²
dy/dx = g(x) is the slope of function y
diffentiate g(x) with respect to x
dg(x)/dx = 6 - 6x = 0
x = 1
again, differentaite with respect to x
d²g(x)/dx² = -6 < 0
hence, g(x) is maximum at x = 1
now,
maximum slope = 2 + 6x - 3x² at x = 1
= 2 + 6(1) -3(1)²
= 2 + 6 - 3
= 5
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