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Question Number 174396 by Best1 last updated on 31/Jul/22

Answered by som(math1967) last updated on 31/Jul/22

$$f^{!}\left(\mathit{x}\right)=2.3^{\mathit{m}\mathit{x}}.{\mathit{s}\mathit{e}\mathit{c}}^2\mathit{x}\mathit{t}\mathit{a}\mathit{n}\mathit{x}+m{3}^{mx}ln3{sec}^{2}x$$$$\Rightarrow 0+mln3=3\Rightarrow \mathit{m}=\frac{3}{\mathit{l}\mathit{n}3}$$$$\mathit{C}.\frac{3}{l\mathit{n}3}$$$$$$

Answered by Ar Brandon last updated on 01/Aug/22

$$\mathrm{Let}\mathrm{the}\mathrm{equation}\mathrm{be}{\mathrm{y}}_{\mathrm{t}}=\mathrm{m}x+c=3x+1$$$$\Rightarrow \mathrm{f}{}^{\prime }\left(x\right)=\mathrm{m}$$$$\mathrm{f}{}^{\prime }\left(x\right)=3^{mx}\left({2\sec }^{2}x\tan x\right)+\left(m{3}^{mx}\ln 3\right){\sec }^{2}x$$$$f{}^{\prime }\left(0\right)=3\Rightarrow f{}^{\prime }\left(0\right)=m\ln 3=3\Rightarrow m=\frac{3}{\ln 3}$$

Commented by Best1 last updated on 31/Jul/22

$$whyyouderivatetheequationof$$$$theliney=3x+1?becausetheslop$$$$oftheis3not1okay$$

Commented by som(math1967) last updated on 31/Jul/22

$$y=3x+1\Rightarrow slopeoftanjent=3thenhow$$$$mln3=1?$$$$$$

Commented by Ar Brandon last updated on 01/Aug/22

$${\mathrm{You}}^{\prime }\mathrm{re}\mathrm{right}!\mathrm{Thanks}.$$

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