Advertisements
Advertisements
प्रश्न
Select the correct answer from the given alternative:
If f(x) `{:(= 2x + 6, "for" 0 ≤ x ≤ 2),(= "a"x^2 + "b"x, "for" 2 < x ≤4):}` is differentiable at x = 2 then the values of a and b are
पर्याय
a = `- 3/2`, b = 3
a = `3/2`, b = 8
a = `1/2`, b = 8
a = `- 3/2`, b = 8
उत्तर
a = `- 3/2`, b = 8
Explanation;
f(x) `{:(= 2x + 6,"," 0 ≤ x ≤ 2),(= "a"x^2 + "b"x,"," 2 < x ≤4):}`
Lf'(2) = 2, Rf'(2) = 2a (2) + b
∵ Lf'(2) = Rf'(2) .......[f is differentiable]
∴ 2 = 4a + b …(i)
∴ f is continuous
∴ `lim_(x -> 2^+) "f"(x) = "f"(2) = lim_(x -> 2^-) "f"(x)`
∴ 4a + 2b = 2(2) + 6
∴ 4a + 2b = 10
∴ 2a + b = 5 …(ii)
Solving (i) and (ii),
a = `-3/2`, b = 8
APPEARS IN
संबंधित प्रश्न
Find the derivative of the following function w.r.t. x.:
x–9
Find the derivative of the following functions w. r. t. x.:
`x^(3/2)`
Find the derivative of the following function w. r. t. x.:
35
Differentiate the following w. r. t. x. : `x sqrtx + logx − e^x`
Differentiate the following w. r. t. x. : `x^(5/2) + 5x^(7/5)`
Differentiate the following w. r. t. x. : `2/7 x^(7/2) + 5/2 x^(2/5)`
Differentiate the following w. r. t. x. : `sqrtx (x^2 + 1)^2`
Differentiate the following w. r. t. x. : x3 log x
Differentiate the following w. r. t. x. : `x^(5/2) e^x`
Differentiate the following w. r. t. x. : ex log x
Differentiate the following w. r. t. x. : x3 .3x
Find the derivative of the following w. r. t. x by using method of first principle:
e2x+1
Find the derivative of the following w. r. t. x by using method of first principle:
log (2x + 5)
Find the derivative of the following w. r. t. x by using method of first principle:
tan (2x + 3)
Find the derivative of the following w. r. t. x by using method of first principle:
sec (5x − 2)
Find the derivative of the following w. r. t. x by using method of first principle:
`x sqrt(x)`
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
tan x at x = `pi/4`
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
`2^(3x + 1)` at x = 2
Show that f(x) = x2 is continuous and differentiable at x = 0
Discuss the continuity and differentiability of f(x) at x = 2
f(x) = [x] if x ∈ [0, 4). [where [*] is a greatest integer (floor) function]
If f(x) `{:(= sin x - cos x, "if" x ≤ pi/2),(= 2x - pi + 1, "if" x > pi /2):}` Test the continuity and differentiability of f at x = `π/2`
Examine the function
f(x) `{:(= x^2 cos (1/x)",", "for" x ≠ 0),(= 0",", "for" x = 0):}`
for continuity and differentiability at x = 0
Determine whether the following function is differentiable at x = 3 where,
f(x) `{:(= x^2 + 2"," , "for" x ≥ 3),(= 6x - 7"," , "for" x < 3):}`
Determine the values of p and q that make the function f(x) differentiable on R where
f(x) `{:( = "p"x^3",", "for" x < 2),(= x^2 + "q"",", "for" x ≥ 2):}`
Determine all real values of p and q that ensure the function
f(x) `{:( = "p"x + "q"",", "for" x ≤ 1),(= tan ((pix)/4)",", "for" 1 < x < 2):}` is differentiable at x = 1
Discuss whether the function f(x) = |x + 1| + |x – 1| is differentiable ∀ x ∈ R
Test whether the function f(x) `{:(= x^2 + 1",", "for" x ≥ 2),(= 2x + 1",", "for" x < 2):}` is differentiable at x = 2
If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1
