Question

ᴅᴇᴛᴇʀᴍɪɴᴇ ᴛʜᴇ ᴀɴᴛɪᴅᴇʀɪᴠᴀᴛɪᴠᴇ ғ ᴏғ “ғ” , ᴡʜɪᴄʜ ɪs ᴅᴇғɪɴᴇᴅ ʙʏ ғ (x) = 4x3 – 6, ᴡʜᴇʀᴇ ғ (0) = 3​

Answer 1

Answer:

ⁱⁿᵗᵉᵍʳᵃᵗᵉ ᵗʰᵉ ᶠᵘⁿᶜᵗⁱᵒⁿ: ∫4ˣ3 – 6 = 4(ˣ4/4)-6ˣ + ᴄ ∫4ˣ3 – 6 = ˣ4 – 6ˣ + ᴄ ᴛʰᵘˢ, ᵗʰᵉ ᵃⁿᵗⁱᵈᵉʳⁱᵛᵃᵗⁱᵛᵉ ᵒᶠ ᵗʰᵉ ᶠᵘⁿᶜᵗⁱᵒⁿ, ғ ⁱˢ ˣ4 – 6ˣ + ᴄ, ʷʰᵉʳᵉ ᴄ ⁱˢ ᵃ ᶜᵒⁿˢᵗᵃⁿᵗ ᴀˡˢᵒ, ᵍⁱᵛᵉⁿ ᵗʰᵃᵗ, ғ(0) = 3, ɴᵒʷ, ˢᵘᵇˢᵗⁱᵗᵘᵗᵉ ˣ = 0 ⁱⁿ ᵗʰᵉ ᵒᵇᵗᵃⁱⁿᵉᵈ ᵃⁿᵗⁱᵈᵉʳⁱᵛᵃᵗⁱᵛᵉ ᶠᵘⁿᶜᵗⁱᵒⁿ, ʷᵉ ᵍᵉᵗ: (0)4 – 6(0) + ᴄ = 3 ᴛʰᵉʳᵉᶠᵒʳᵉ, ᴄ = 3. ɴᵒʷ, ˢᵘᵇˢᵗⁱᵗᵘᵗᵉ ᴄ = 3 ⁱⁿ ᵃⁿᵗⁱᵈᵉʳⁱᵛᵃᵗⁱᵛᵉ ᶠᵘⁿᶜᵗⁱᵒⁿ.

Answer 2

Answer:

Given Function :ᶠ (ˣ) = 4ˣ3 – 6 ɴow,integrate the function.. ∫4ˣ3 – 6 = 4(ˣ4/4)-6ˣ + ᴄ ∫4ˣ3 – 6 = ˣ4 – 6ˣ + ᴄ ᴛhus, the antiderivative function is the , ғ ⁱˢ ˣ4 – 6ˣ + ᴄ, where ᴄ is a constant ᴀlso, given that , ғ(0) = 3, ɴow, substitute ˣ = 0 in the antiderivative function ,we get (0)4 – 6(0) + ᴄ = 3 ᴛherefore, ᴄ = 3. ɴow, substitute ᴄ = 3 ⁱⁿ antiderivative function Hence, the required antiderivative function isˣ4 – 6ˣ + 3 ʜᵒᵖᵉ ⁱᵗ'ˢ ʰᵉˡᵖ ᵘʰ ❤️ #BrainlyCelb ✔️