Advertisements
Advertisements
प्रश्न
Discuss extreme values of the function f(x) = x.logx
Advertisements
उत्तर
f(x) = x.logx
Differentiating w.r.t. x,
`f'(x) = x . 1/x + logx.1`
f'(x) = 1 + logx
Differentiating again w.r.t. x,
`f''(x) = 1/x`
For maxima or minima,
f'(x) = 0
∴ 1 + logx = 0
∴ logx = -1
∴ x = `e^-1`
∴ `f''(1/e) = 1/(1/e)`
∴ `f''(1/e) = e`
∴ `f''(1/e) > 0`
∴ f(x) is minimum at x = `1/e`
APPEARS IN
संबंधित प्रश्न
Find dy/dx if x sin y + y sin x = 0.
Find `bb(dy/dx)` in the following:
ax + by2 = cos y
if `(x^2 + y^2)^2 = xy` find `(dy)/(dx)`
If \[f\left( x \right) = x^3 + 7 x^2 + 8x - 9\]
, find f'(4).
Differentiate e4x + 5 w.r..t.e3x
Differentiate tan-1 (cot 2x) w.r.t.x.
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
Find `"dy"/"dx"` if : x = t2 + t + 1, y = `sin((pit)/2) + cos((pit)/2) "at" t = 1`
Find the nth derivative of the following : sin (ax + b)
Choose the correct option from the given alternatives :
If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........
Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0
Find `"dy"/"dx"` if, yex + xey = 1
If `"x"^5 * "y"^7 = ("x + y")^12` then show that, `"dy"/"dx" = "y"/"x"`
Solve the following:
If `"e"^"x" + "e"^"y" = "e"^((x + y))` then show that, `"dy"/"dx" = - "e"^"y - x"`.
If `"x"^"a"*"y"^"b" = ("x + y")^("a + b")`, then show that `"dy"/"dx" = "y"/"x"`
If x2 + y2 = 1, then `(d^2x)/(dy^2)` = ______.
Find `(dy)/(dx)` if x + sin(x + y) = y – cos(x – y)
Let y = y(x) be a function of x satisfying `ysqrt(1 - x^2) = k - xsqrt(1 - y^2)` where k is a constant and `y(1/2) = -1/4`. Then `(dy)/(dx)` at x = `1/2`, is equal to ______.
If y = `sqrt(tan x + sqrt(tanx + sqrt(tanx + .... + ∞)`, then show that `dy/dx = (sec^2x)/(2y - 1)`.
Find `dy/dx` at x = 0.
If y = `(x + sqrt(x^2 - 1))^m`, show that `(x^2 - 1)(d^2y)/(dx^2) + xdy/dx` = m2y
