WebThe minimum value of any quadratic expression ax 2 + bx + c = 0, (when a > 0) is -D/4a. Where, D = b 2 - 4ac. Calculation: Here, a, b and c is 4, -5 and 1 respectively. So, D = (-5) 2 - … Webfor x to be real, discriminant should be greater than or equal to zero, Hence, the minimum value of x+2x 2+2x+4 is 2.

If x ∈ R , find the minimum value of the expression 3^x + 3^1 - x

WebMar 23, 2024 · Transcript. Example 31 (Method 1) Find local minimum value of the function f given by f (𝑥) = 3 + 𝑥 , 𝑥 ∈ R. f (𝑥) = 3 + 𝑥 Since Value of 𝒙 ≥𝟎 So, Minimum value of 𝑥 =0 Now, Minimum value of f (𝑥) = 3 + Minimum value of 𝑥 = 3 + 0 = 3 Hence minimum value of f (𝑥) = 3 Example 31 (Method 2) Find local ... WebFeb 5, 2024 · Find the minimum value of 4x + 41−x, x ∈ R. LIVE Course for free. Rated by 1 million+ students Get app now Login. Remember. Register; Test; JEE; NEET; Home; Q&A; … fire resistant wood paneling

The minimum value of 4^x + 4^1 - x, xepsilon R , is - Toppr

Weband f0(x) > 0 (meaning f is increasing) on the intervals (π/2,3π/2). (b) Find the local maximum and minimum values of f. Answer: f0(x) = 0 when either cosx = 0 or sinx = −1, which is to say when x = π/2,3π/2. f0 changes from negative to positive at x = π/2 so, by the first derivative test, the local minimum value of f is WebTo get maximum and minimum values of the function substitute x = a and x = b in f (x). Maximum value = f (a) Minimum value = f (b) Maximum and Minimum Values of a Function Using Derivatives Example 1 : Determine the maximum value of the function : f (x) = 4x - x2 + 3 Solution : Find the first derivative of f (x). f' (x) = 4 (1) - 2x + 0 = 4 - 2x WebSolution. Since. Arithmetic mean ≥ geometric mean of 4 x and 4 1 – x. i. e 4 x + 4 1 - x 2 ≥ 4 x. 4 1 - x i. e 4 x + 4 1 - x 2 ≥ 4 x. 4. 4 - x i. e 4 x + 4 1 - x 2 ≥ 2 i. e 4 x + 4 1 - x ≥ 2 × 2 = 4. i.e … ethnic painting