Find the value of x at the minimum point of the curve y =...
Find the value of x at the minimum point of the curve y = x3 + x2 - x + 1
\(\frac{1}{3}\)
-\(\frac{1}{3}\)
1
-1
Correct answer is A
y = x3 + x2 - x + 1
\(\frac{dy}{dx}\) = \(\frac{d(x^3)}{dx}\) + \(\frac{d(x^2)}{dx}\) - \(\frac{d(x)}{dx}\) + \(\frac{d(1)}{dx}\)
\(\frac{dy}{dx}\) = 3x2 + 2x - 1 = 0
\(\frac{dy}{dx}\) = 3x2 + 2x - 1
At the maximum point \(\frac{dy}{dx}\) = 0
3x2 + 2x - 1 = 0
(3x2 + 3x) - (x - 1) = 0
3x(x + 1) -1(x + 1) = 0
(3x - 1)(x + 1) = 0
therefore x = \(\frac{1}{3}\) or -1
For the maximum point
\(\frac{d^2y}{dx^2}\) < 0
\(\frac{d^2y}{dx^2}\) 6x + 2
when x = \(\frac{1}{3}\)
\(\frac{dx^2}{dx^2}\) = 6(\(\frac{1}{3}\)) + 2
= 2 + 2 = 4
\(\frac{d^2y}{dx^2}\) > o which is the minimum point
when x = -1
\(\frac{d^2y}{dx^2}\) = 6(-1) + 2
= -6 + 2 = -4
-4 < 0
therefore, \(\frac{d^2y}{dx^2}\) < 0
the minimum point is 1/3
Find the simple interest rate percent per annum at which N1,000 accumulates to N1,240 in 3 years...
If x : y = 3 : 2 and y : z = 5 : 4, find the value of x in the ratio x : y : z ...
From a point P, Q is 5km due West and R is12km due South of Q. Find the distance between P...
A rectangle with width \(\frac{3}{4}\)cm and area 3 \(\frac{3}{8}\)cm\(^2\). Find the length...
Find the values of x for which the expression \(\frac{(x - 3)(x - 2)}{x^2 + x - 2}\)...
Integrate \(\int_{-1} ^{2} (2x^2 + x) \mathrm {d} x\)...
From the equation whose roots are x = \(\frac{1}{2}\) and -\(\frac{2}{3}\)...
Find the locus of point equidistant from two straight lines y - 5 = 0 and y - 3 = 0 ...