How do you write the logarithmic equation in exponential form when you use ln?
1 answer:
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Answer:
f''(0.3) > 0 therefore,
x = 0.3 is point of minima
and,
f''(0) = 0
thus,
x = 0 is point of neither maxima nor minima
Step-by-step explanation:
Given function:
f(x) = 5x⁴ − 2x³
Now,
To find the points of maxima or minima, put f'(x) = 0
thus,
f'(x) = (4)5x³ - (3)2x² = 0
or
20x³ - 6x² = 0
or
x(20x² - 6x) = 0
or
x = 0 and 20x² - 6x = 0
or
x = 0 and 2x(10x - 3) = 0
or
x = 0 and 2x = 0 and (10x - 3) = 0
or
x = 0 and x = 0 and x = = 0.3
thus,
condition for maxima or minima
f''(x) = (3 × 4)5x² - (2 × 3)2x
or
f''(x) = 60x² - 12x
at
x = 0
f''(0) = 60(0)² - 12(0) = 0
at x = 0.3
f''(0.3) = 60(0.3)² - 12(0.3)
= 5.4 - 3.6
= 1.8
since,
f''(0.3) > 0 therefore,
x = 0.3 is point of minima
and,
f''(0) = 0
thus,
x = 0 is point of neither maxima nor minima