Let $$f(x)$$ be a function such that,$$f(0)=f$$′$$(0)=0$$ ,f′′$$(x)=sec4$$⁡ $$x+4$$ then the function is

Question

Let $$f(x)$$ be a function such that,$$f(0)=f$$′$$(0)=0$$ ,f′′$$(x)=sec4$$⁡ $$x+4$$ then the function is

Infinity Learn · Accepted Answer

Since,f′′$$(x)=sec4$$⁡ $$x+4f$$′′$$(x)=1+tan2$$ ⁡$$xsec2$$⁡ $$x+4$$⇒ f′$$(x)=$$$$tan$$ ⁡$$x+tan3$$ ⁡$$x3+4x+C$$⇒f′$$(0)=0$$⇒$$0=C$$ Then, f′$$(x)=$$$$tan$$ ⁡$$x+tan3$$ ⁡$$x3+4xf$$′$$(x)=$$$$tan$$ ⁡$$x+tan3$$  ⁡$$x3+4x=$$$$tan$$ ⁡$$x+13tan$$⁡ $$xsec2$$⁡x−$$1+4x$$⇒ f′$$(x)=23tan$$ ⁡$$x+13tan$$ ⁡$$xsec2$$ ⁡$$x+4x$$∴ $$f(x)=23log$$⁡ |$$sec$$ ⁡x|$$+tan2$$ ⁡$$x6+2x2+d$$ But  $$f(0)=0$$⇒$$d=0$$ Then, $$f(x)=23log$$ ⁡|$$sec$$ ⁡x|$$+16tan2$$ ⁡$$x+2x2$$

Let f(x) be a function such that, $f (0) = f^{'} (0) = 0$ , $f^{''} (x) = \sec^{4} x + 4$ then the function is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Let f(x) be a function such that,f(0)=f′(0)=0 ,f′′(x)=sec4⁡ x+4 then the function is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Let f(x) be a function such that, $f (0) = f^{'} (0) = 0$ , $f^{''} (x) = \sec^{4} x + 4$ then the function is