Find the intervals in which the following functions are increasing or decreasing.(i) f(x) = 10 − 6x − 2x2(ii) f(x) = x2 + 2x − 5(iii) f(x) = 6 − 9x − x2(iv) f(x) = 2x3 − 12x2 + 18x + 15(v) f(x) = 5 + 36x + 3x2 − 2x3(vi) f(x) = 8 + 36x + 3x2 − 2x3(vii) f(x) = 5x3 − 15x2 − 120x + 3(viii) f(x) = x3 − 6x2 − 36x + 2(ix) f(x) = 2x3 − 15x2 + 36x + 1(x) f(x) = 2x3 + 9x2 + 12x + 20(xi) f(x) = 2x3 − 9x2 + 12x − 5(xii) f(x) = 6 + 12x + 3x2 − 2x3(xiii) f(x) = 2x3 − 24x + 107(xiv) f(x) = −2x3 − 9x2 − 12x + 1(xv) f(x) = (x − 1) (x − 2)2(xvi) f(x) = x3 − 12x2 + 36x + 17(xvii) f(x) = 2x3 − 24x + 7(xviii) fx=310x4-45x3-3x2+365x+11(xix) f(x) = x4 − 4x(xx) fx=x44+23x3-52x2-6x+7(xxi) f(x) = x4 − 4x3 + 4x2 + 15(xxii) f(x) = 5x32-3x52, x > 0(xxiii) f(x) = x8 + 6x2(xxiv) f(x) = x3 − 6x2 + 9x + 15(xxv) fx=x(x-2)2(xxvi) fx=3x4-4x3-12x2+5(xxvii) fx=32x4-4x3-45x2+51(xxviii) fx=log2+x-2x2+x, x∈R(xxix) fx=x44-x3-5x2+24x+12

Find the intervals in which the following functions are increasing or

1.	Find the intervals in which the following functions are increasing or decreasing.(i) f(x) = 10 − 6x − 2x2(ii) f(x) = x2 + 2x − 5(iii) f(x) = 6 − 9x − x2(iv) f(x) = 2x3 − 12x2 + 18x + 15(v) f(x) = 5 + 36x + 3x2 − 2x3(vi) f(x) = 8 + 36x + 3x2 − 2x3(vii) f(x) = 5x3 − 15x2 − 120x + 3(viii) f(x) = x3 − 6x2 − 36x + 2(ix) f(x) = 2x3 − 15x2 + 36x + 1(x) f(x) = 2x3 + 9x2 + 12x + 20(xi) f(x) = 2x3 − 9x2 + 12x − 5(xii) f(x) = 6 + 12x + 3x2 − 2x3(xiii) f(x) = 2x3 − 24x + 107(xiv) f(x) = −2x3 − 9x2 − 12x + 1(xv) f(x) = (x − 1) (x − 2)2(xvi) f(x) = x3 − 12x2 + 36x + 17(xvii) f(x) = 2x3 − 24x + 7(xviii) fx=310x4-45x3-3x2+365x+11(xix) f(x) = x4 − 4x(xx) fx=x44+23x3-52x2-6x+7(xxi) f(x) = x4 − 4x3 + 4x2 + 15(xxii) f(x) = 5x32-3x52, x > 0(xxiii) f(x) = x8 + 6x2(xxiv) f(x) = x3 − 6x2 + 9x + 15(xxv) fx=x(x-2)2(xxvi) fx=3x4-4x3-12x2+5(xxvii) fx=32x4-4x3-45x2+51(xxviii) fx=log2+x-2x2+x, x∈R(xxix) fx=x44-x3-5x2+24x+12
Answer» Find the intervals in which the following functions are increasing or decreasing. (i) f(x) = 10 − 6x − 2x² (ii) f(x) = x² + 2x − 5 (iii) f(x) = 6 − 9x − x² (iv) f(x) = 2x³ − 12x² + 18x + 15 (v) f(x) = 5 + 36x + 3x² − 2x³ (vi) f(x) = 8 + 36x + 3x² − 2x³ (vii) f(x) = 5x³ − 15x² − 120x + 3 (viii) f(x) = x³ − 6x² − 36x + 2 (ix) f(x) = 2x³ − 15x² + 36x + 1 (x) f(x) = 2x³ + 9x² + 12x + 20 (xi) f(x) = 2x³ − 9x² + 12x − 5 (xii) f(x) = 6 + 12x + 3x² − 2x³ (xiii) f(x) = 2x³ − 24x + 107 (xiv) f(x) = −2x³ − 9x² − 12x + 1 (xv) f(x) = (x − 1) (x − 2)² (xvi) f(x) = x³ − 12x² + 36x + 17 (xvii) f(x) = 2x³ − 24x + 7 (xviii) $f (x) = \frac{3}{10} x^{4} - \frac{4}{5} x^{3} - 3 x^{2} + \frac{36}{5} x + 11$ (xix) f(x) = x⁴ − 4x (xx) $f (x) = \frac{x^{4}}{4} + \frac{2}{3} x^{3} - \frac{5}{2} x^{2} - 6 x + 7$ (xxi) f(x) = x⁴ − 4x³ + 4x² + 15 (xxii) f(x) = $5 x^{\frac{3}{2}} - 3 x^{\frac{5}{2}}$ , x > 0 (xxiii) f(x) = x⁸ + 6x² (xxiv) f(x) = x³ − 6x² + 9x + 15 (xxv) $f (x) = {\{x (x - 2)\}}^{2}$ (xxvi) $f (x) = 3 x^{4} - 4 x^{3} - 12 x^{2} + 5$ (xxvii) $f (x) = \frac{3}{2} x^{4} - 4 x^{3} - 45 x^{2} + 51$ (xxviii) $f (x) = \log (2 + x) - \frac{2 x}{2 + x}, x \in R$ (xxix) $f (x) = \frac{x^{4}}{4} - x^{3} - 5 x^{2} + 24 x + 12$

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