Answer on Question #49865 – Math – Calculus
Given: x^2[f(x)]^2=9; and f9-10=3 Find f''(-1) by implicit differentiation.
Solution
𝒙𝟐 𝒇(𝒙)𝟐 = 𝟗 →
→ 𝒇′ (𝒙) = −
𝒇
′′ (𝒙)
𝒅 𝟐
𝒅
[𝒙 𝒇(𝒙)𝟐 ] =
(𝟗) → 𝟐𝒙𝒇𝟐 + 𝟐𝒙𝟐 𝒇𝒇′ = 𝟎 →
𝒅𝒙
𝒅𝒙
𝒇(𝒙)
𝒙
𝒇′ (𝒙) 𝒇(𝒙)
𝒇(𝒙)
=−
+ 𝟐 =𝟐 𝟐
𝒙
𝒙
𝒙
𝒇′′ (−𝟏) = 𝟐
𝟑
=𝟔
(−𝟏)𝟐
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