Find the intervals in which the following functions are: (i) increasing (ii) decreasing. (a) `f(x) = 10-6x+x^(2)` (b) `f(x) = 2x^(2)-6x` (c) `f(x) = 2
Find the intervals in which the following functions are:
(i) increasing
(ii) decreasing.
(a) `f(x) = 10-6x+x^(2)`
(b) `f(x) = 2x^(2)-6x`
(c) `f(x) = 2x^(3)-3x^(2)-36x+1`
(d) `f(x)=x^(3)+2x^(2)+x-1`
`(e) f(x)= 4x+1/x,x ne 0`
(f) `f(x)=2x^(3)-9x^(2)+12x+1`
(g) `f(x)= 5+36x+3x^(2)-2x^(3)`
(h) `f(x) = (x+2)^(3)(x-3)^(3)`
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Correct Answer - `(a)(i) [3,infty[" "(ii)]-infty, 3]`
`(b) (i)[3/2,infty[" "(ii)]-infty,3/2]`
`(c)(i)]-infty,-2]cup[3,infty[" "(ii)[-2,3]`
`(d)(i)]-infty,-1/3] cup[-1,infty[" "(ii)[-1,-1/3]`
`(e)(i)]-infty,-1/2]cup[1/2,infty[" "(ii)[-1/2,1/2]-{0}`
`(f)(i)]-infty,1]cup[2,infty[" "(ii) [1, 2]`
`(g)(i)[-2,3]" "(ii)]-infty,-2]cup[3,infty[`
`(h)(i)[1/2,infty[" "(ii)]-infty,1/2]`
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